If a, 8, b are in AP, a, 4, b are in GP, and if a, x, b are in HP then x is

(a)

2

(b)

1

(c)

4

(d)

16

The HM of two positive numbers whose AM and GM are 16, 8 respectively is

(a)

10

(b)

6

(c)

5

(d)

4

The n^th term of the sequence 1, 2, 4, 7, 11,... is

(a)

n³ + 3n² + 2n

(b)

n³ - 3n² + 3n

(c)

\(\frac { n(n+1)(n+2) }{ 3 } \)

(d)

\(\frac { { n }^{ 2 }-n+2 }{ 2 } \)

The sum of an infinite GP is 18. If the first term is 6, the common ratio is

(a)

\(\frac { 1 }{ 3 } \)

(b)

\(\frac { 2 }{ 3 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

\(\frac { 3 }{ 4 } \)

If the sum of n terms of an A. P. be 3n² - n and its common difference is 6, then its first term is ______________

(a)

2

(b)

3

(c)

1

(d)

4

The term without x in \({ \left( 2x-\frac { 1 }{ 2{ x }^{ 2 } } \right) }^{ 12 }\) is ______________

(a)

495

(b)

-495

(c)

-7920

(d)

7920

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be ______________

(a)

5

(b)

6

(c)

7

(d)

8

If in an infinite G. P. first term is equal to 10 times the sum of all successive terms, then its common ratio is ______________

(a)

\(\frac { 1 }{ 10 } \)

(b)

\(\frac { 1 }{ 11 } \)

(c)

\(\frac { 1 }{ 9 } \)

(d)

\(\frac { 1 }{ 20 } \)

The nth term of a G.P is 128 and the sum of its n terms is 225. If its common ratio is 2, then its first term is ______________

(a)

1

(b)

3

(c)

8

(d)

none of these 

The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27}}\),\(\infty \) is ______________

(a)

1

(b)

3

(c)

9

(d)

none of these